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Shrieking Rod
Prof. Chih-Ta Chia
Dept. of Physics NTNU
Problem # 13
Shrieking rodA metal rod is held between two fingers
and hit. Investigate how the sound produced depends on the position of holding and hitting the rod?
Vibration in rod? How did you create vibrations in the rod? Three type of vibrations are created simply by hitting
the rod: Longitudinal, torsional and flexural vibrations. Longitudinal and Flexural vibrations are most likely to
last longer, but not the torsional vibrations. What are the resonance conditions for these three
vibrations? What are the speeds of these three vibrations that
travel in the rod. How to determine the wave velocity?
Vibration of Rod?
What is the damping effect on the longitudinal and vibrations? Hitting position dependence? Time dependence?
Longitudinal wave damping and flexural vibration damping? Which one is damped fast?
Cylindrical Rod : Longitudinal and Torsional wave
E
Cl Longitudinal wave speedE: Young’s Modulus
Torsional wave speed: Shear Modulus
tC
Passion Ratio : 12
1 2
t
l
f
f
Young’s Modulus
A
FS
Stress: S
Longitudinal Strain: Stl
lSt
Young’s Modulus: EtS
SY
L
LStrain
A
FStress
Hook’s Law
L
LY
A
F
Stress is proportional to Strain.
Stress, Strain and Hook’s Law
Shear Modulus The shear modulus is the elastic modulus we use for the deformation which takes place when a force is applied parallel to one face of the object while the opposite face is held fixed by another equal force.
L
L
A
F
Shear Modulus:
LxA
F
StrainShear
StressShear
Resonance : When Clamped in the Middle
L
Cnf l
nl 212
L
Cnf t
nt 212
3, 2, 1, 0,n
Speed of wave in Rod
Flexural VibrationsEquation of Motion : (Length L and radius a)
2
2
4
422
t
y
x
ycl
cl is the velocity of longitudinal waves in an infinitely long bar.
The radius of gyration is defined as above. For the circular rod, is half the bar’s radius. As for the square rod, is D/√12.
dAyA
22 1
Y
cl 2